Try putting that dimension on the Page shelf - Tableau can automatically print all page views as pages into one PDF.
There could be undesirable side effects, though, depending on the data and sheet layout.
Is this the only way to print one document with multiple filters? What are the undesireable side effects?
The undesirable side effects would be due to the way the page shelf works - it creates place-holders for all possible combinations of dimensions on the sheet, so it may have a lot of blank cells.
For example, this view uses filter, but you need to select each product manually to print all product pages:
While this view uses page, and you can set it up in such a way that it will print all products at once, one product per page, but you get blank cells for states where this product is not sold:
This may be something you do or do not want, depending on your situation.
This is a great solution, however it didn't help me unfortunately.
I was unclear with my problem description - I use parameter as filter and when I put on the Page shelf it cannot change automatically I think. Maybe I'm wrong.